On subgroups of $ZJ$ type of an $\goth F$-injector for fitting classes $\goth F$ between $\goth E_{p^*p}$ and $\goth E_{p^*}\goth S_p$

A. Martínez Pastor

Resum

Let $G$ be a finite group and $p$ a prime. We consider an $\goth F$-injector $K$ of $G$, being $\goth F$ a Fitting class between $\goth E_{p^*p}$ and $\goth E_{p^*}\goth S_p$, and we study the structure and normality in $G$ of the subgroups $ZJ(K)$ and $ZJ^*(K)$, provided that $G$ verify certain conditions, extending some results of G. Glauberman (A characteristic subgroup of a $p$-stable group, Canad. J. Math. 20 (1968), 555--564).